Monday, September 9, 2013

Reliable Research

The mathematician Frank Quinn argues that one of the distinguishing features of mathematics since about 1950 was highly reliable error-displaying methods--rigorous proof. Intuition and pictures were no substitute for rigorous proofs, and in general they could be misleading. If you made an error in a modern proof, it would be displayed, that is, other mathematicians would  eventually find it, even if your result were eventually shown to be true by a rigorous proof.

In the kind of work most people do in the scholarly realm, there is no such sure-fire method. There are lots of good practices--use of sources, references, generation and use of data; and if you have made some sort of error it is likely that other readers, your competitors so to speak, are likely to discover them. But usually we are so wrapped up on our work, it is hard for us to discover such errors. In mathematics, on the other hand, mathematicians find errors in their ongoing work all the time, and so improve their proofs.

I am assuming good will and ethical behavior, although in fact that is not always the case.

On the other hand, if you violate good practices: plagiarism, faked data, poor arguments, you will be skewered.

Quinn also points out that modern methods allow ordinary mathematicians to make contributions, since even if they do not have "intuition" of a high order, they can know if their work is rigorous.

No comments: